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Jun 27, 2018
06/18

by
G. Fuhrmann; M. Gröger; T. Jäger

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We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For instance, it gives positive value to Denjoy examples on the circle and Sturmian subshifts, while being zero for all isometries and Morse-Smale systems. After discussing basic properties and examples, we show that amorphic complexity and the underlying asymptotic...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1503.01036

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3.0

Jun 29, 2018
06/18

by
Xudong Chen; Mohamed-Ali Belabbas; Tamer Basar

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A cluster consensus system is a multi-agent system in which the autonomous agents communicate to form multiple clusters, with each cluster of agents asymptotically converging to the same clustering point. We introduce in this paper a special class of cluster consensus dynamics, termed the $G$-clustering dynamics for $G$ a point group, whereby the autonomous agents can form as many as $|G|$ clusters, and moreover, the associated $|G|$ clustering points exhibit a geometric symmetry induced by the...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1601.06346

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12

Jun 26, 2018
06/18

by
Lewis Bowen; Alexander Bufetov; Olga Romaskevich

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Mean convergence of Markovian spherical averages is established for a measure-preserving action of a finitely-generated free group on a probability space. We endow the set of generators with a generalized Markov chain and establish the mean convergence of resulting spherical averages in this case under mild nondegeneracy assumptions on the stochastic matrix $\Pi$ defining our Markov chain. Equivalently, we establish the triviality of the tail sigma-algebra of the corresponding Markov operator....

Topics: Mathematics, Dynamical Systems, Probability, Group Theory

Source: http://arxiv.org/abs/1502.01797

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Jun 26, 2018
06/18

by
Tomasz Downarowicz; Eli Glasner

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If $\pi:(X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\pi$ is also a measure-theoretic isomorphism. We consider the case when the systems are minimal and we pay special attention to equicontinuous $(Z,S)$. We first establish a characterization of this type of isomorphic extensions in terms of mean equicontinuity, and then show that an isomorphic extension need not be almost...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1502.06999

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3.0

Jun 29, 2018
06/18

by
Stephan De Bievre; Simona Rota Nodari

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We consider the orbital stability of the relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and show how it allows to prove the local coercivity of the Lyapunov function, which in turn implies orbital stability. The method is applied to study the orbital stability of the plane waves of a system of...

Topics: Symplectic Geometry, Dynamical Systems, Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1605.02523

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3.0

Jun 30, 2018
06/18

by
C. Efthymiopoulos; G. Contopoulos; M. Katsanikas

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It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry 1926, Moser 1956, 1958, Giorgilli 2001). The unstable and stable manifolds intersect at an infinity of homoclinic points, generating a complicated homoclinic tangle. In the case of simple mappings it was found (Da Silva Ritter et al. 1987) that the domain of convergence of the formal series extends to infinity along the invariant...

Topics: Nonlinear Sciences, Astrophysics, Chaotic Dynamics, Mathematics, Earth and Planetary Astrophysics,...

Source: http://arxiv.org/abs/1404.7679

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3.0

Jun 30, 2018
06/18

by
C. García-Azpeitia

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In this paper we present a summary of the last works of Jorge Ize regarding the global bifurcation of periodic solutions from the equilibria of a satellite attracted by n primary bodies. We present results on the global bifurcation of periodic solutions for the primary bodies from the Maxwell's ring, in the plane and in space, where n identical masses on a regular polygon and one central mass are turning in a plane at a constant speed. The symmetries of the problem are used in order to find the...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1403.5595

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Jun 30, 2018
06/18

by
Steven Hurder; Olga Lukina

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A weak solenoid is a foliated space defined as the inverse limit of finite coverings of a closed compact manifold $M$. The monodromy of a weak solenoid defines an equicontinuous minimal action on a Cantor space $X$ by the fundamental group $G$ of $M$. The discriminant group of this action is an obstruction to this action being homogeneous. The discriminant vanishes if the group $G$ is abelian, but there are examples of actions of nilpotent groups for which the discriminant is non-trivial. The...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1702.03032

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4.0

Jun 29, 2018
06/18

by
Nithin Govindarajan; Hassan Arbabi; Louis van Blargian; Timothy Matchen; Emma Tegling; Igor Mezić

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We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick under certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism carried out by Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by means of...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1608.08734

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3.0

Jun 30, 2018
06/18

by
Kathryn Mann

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We show that the group of germs at infinity of orientation-preserving homeomorphisms of R admits no action on the line. This gives an example of a left-orderable group of the same cardinality as Homeo+(R) that does not embed in Homeo+(R). As an application of our techniques, we construct a finitely generated group of germs that does not extend to Homeo+(R) and, separately, extend a theorem of E. Militon on homomorphisms between groups of homeomorphisms.

Topics: Group Theory, Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1406.5575

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4.0

Jun 29, 2018
06/18

by
Thomas Gauthier; Gabriel Vigny

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In analogy to the equidistribution of preimages of a prescribed point by the iterates of a polynomial map in the complex plane towards the equilibrium measure, we show here the equidistribution of points for which the derivative of the n-th iterate of the polynomial takes a suitable prescribed value towards the equilibrium measure. We then give a similar statement in the space of degree d polynomials for the equidistribution of parameters for which the n-derivative at a given critical value has...

Topics: Complex Variables, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1606.05422

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4.0

Jun 29, 2018
06/18

by
Mauro Rosestolato

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We study path-dependent SDEs in Hilbert spaces. By using methods based on contractions in Banach spaces, we prove existence and uniqueness of mild solutions, continuity of mild solutions with respect to perturbations of all the data of the system, G\^ateaux differentiability of generic order n of mild solutions with respect to the starting point, continuity of the G\^ateaux derivatives with respect to all the data. The analysis is performed for generic spaces of paths that do not necessarily...

Topics: Probability, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1606.06321

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5.0

Jun 30, 2018
06/18

by
Daniel Karrasch; Florian Huhn; George Haller

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Coherent boundaries of Lagrangian vortices in fluid flows have recently been identified as closed orbits of line fields associated with the Cauchy-Green strain tensor. Here we develop a fully automated procedure for the detection of such closed orbits in large-scale velocity data sets. We illustrate the power of our method on ocean surface velocities derived from satellite altimetry.

Topics: Physics, Fluid Dynamics, Mathematics, Computing Research Repository, Atmospheric and Oceanic...

Source: http://arxiv.org/abs/1404.3109

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4.0

Jun 30, 2018
06/18

by
John Cleveland

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In \cite{ CLEVACKTHI, CLEVACK} an attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness, asymptotic analysis and parameter estimation for fully nonlinear evolutionary game models. A theory is developed as a dynamical system on the state space of finite signed Borel measures under the weak star topology. Two drawbacks of the previous theory is that the techniques and machinery involved in establishing the results are awkward and...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1409.3907

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5.0

Jun 29, 2018
06/18

by
Magnus Aspenberg; Tomas Persson

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We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target property. This generalises several similar results for $\beta$-transformations to more general non-linear families. The proofs are based on a result by Schnellmann on typicality in parametrised families.

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1603.01116

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4.0

Jun 30, 2018
06/18

by
Gregory Kelsey; Russell Lodge

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We use the theory of self-similar groups to enumerate all combinatorial classes of non-exceptional quadratic Thurston maps with fewer than five postcritical points. The enumeration relies on our computation that the corresponding maps on moduli space can be realized by quadratic rational maps with fewer than four postcritical points.

Topics: Group Theory, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1704.03929

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2.0

Jun 30, 2018
06/18

by
Maximilien Gadouleau; Adrien Richard; Søren Riis

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In this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the number of fixed points that only depends on $D$. We then discover relationships between the number of fixed points of $f$ and problems in coding theory, especially the design of codes for the asymmetric channel. Using these relationships, we derive upper and...

Topics: Mathematics, Discrete Mathematics, Computing Research Repository, Information Theory, Dynamical...

Source: http://arxiv.org/abs/1409.6144

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2.0

Jun 30, 2018
06/18

by
Eleonora Catsigeras; Xueting Tian

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Let $f:M\rightarrow M$ be a $C^1$ diffeomorphism with a dominated splitting on a compact Riemanian manifold $M$ without boundary. We state and prove several sufficient conditions for the topological entropy of $f$ to be positive. The conditions deal with the dynamical behaviour of the (non-necessarily invariant) Lebesgue measure. In particular, if the Lebesgue measure is $\delta$-recurrent then the entropy of $f$ is positive. We give counterexamples showing that these sufficient conditions are...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1409.6107

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2.0

Jun 30, 2018
06/18

by
Mauro Artigiani; Luca Marchese; Corinna Ulcigrai

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We study Lagrange spectra of Veech translation surfaces, which are a generalization of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray. As a main tool, we use the boundary expansion developed by Bowen and Series to code geodesics in the corresponding Teichm\"uller disk and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor sets.

Topics: Mathematics, Number Theory, Dynamical Systems

Source: http://arxiv.org/abs/1409.7023

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3.0

Jun 30, 2018
06/18

by
Lennard Bakker; Skyler Simmons

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We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless particle on the z-axis. The study of the motion of this particle can then be modelled as a time-dependent Hamiltonian System. We give a geometric construction of a surface in the three-dimensional phase space separating orbits for which the massless particle...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1410.2636

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2.0

Jun 30, 2018
06/18

by
Félix A. Miranda; Fernando Castaños; Alexander Poznyak

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The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's...

Topics: Optimization and Control, Mathematics, Systems and Control, Computing Research Repository,...

Source: http://arxiv.org/abs/1412.3861

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2.0

Jun 30, 2018
06/18

by
Dragos Ghioca; Holly Krieger; Khoa Nguyen

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We prove a special case of the Dynamical Andre-Oort Conjecture formulated by Baker and DeMarco. For any integer d>1, we show that for a rational plane curve C parametrized by (t, h(t)) for some non-constant polynomial h with complex coefficients, if there exist infinitely many points (a,b) on the curve C such that both z^d+a and z^d+b are postcritically finite maps, then h(z)=uz for a (d-1)-st root of unity u. As a by-product of our proof, we show that the Mandelbrot set is not the filled...

Topics: Complex Variables, Mathematics, Number Theory, Dynamical Systems

Source: http://arxiv.org/abs/1404.6011

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2.0

Jun 30, 2018
06/18

by
Shuxia Pan

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This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice differential equations without time delay. The minimal wave speed of invasion traveling wave solutions is established by presenting the existence and nonexistence of traveling wave solutions.

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1405.1126

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3.0

Jun 30, 2018
06/18

by
Lilian Matthiesen

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We introduce and analyse a general class of not necessarily bounded multiplicative functions, examples of which include the function $n \mapsto \delta^{\omega (n)}$, where $\delta > 0$ and where $\omega$ counts the number of distinct prime factors of $n$, as well as the function $n \mapsto |\lambda_f(n)|$, where $\lambda_f(n)$ denotes the Fourier coefficients of a primitive holomorphic cusp form. For this class of functions we show that after applying a `$W$-trick' their elements become...

Topics: Mathematics, Number Theory, Combinatorics, Dynamical Systems

Source: http://arxiv.org/abs/1405.1018

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2.0

Jun 30, 2018
06/18

by
Niklas Wahlström; Patrix Axelsson; Fredrik Gustafsson

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Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. We present a novel algorithm using a combination of Lyapunov equations and analytical solutions, enabling efficient implementation in software. The proposed method circumvents numerical problems...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1402.1358

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2.0

Jun 30, 2018
06/18

by
Mohammad Farazmand; George Haller

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We use recent developments in the theory of finite-time dynamical systems to objectively locate the material boundaries of coherent vortices in two-dimensional Navier--Stokes turbulence. We show that these boundaries are optimal in the sense that any closed curve in their exterior will lose coherence under material advection. Through a detailed comparison, we find that other available Eulerian and Lagrangian techniques significantly underestimate the size of each coherent vortex.

Topics: Fluid Dynamics, Mathematics, Physics, Geophysics, Dynamical Systems

Source: http://arxiv.org/abs/1402.4835

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2.0

Jun 30, 2018
06/18

by
Piet Van Mieghem

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Exploiting the power of the expectation operator and indicator (or Bernoulli) random variables, we present the exact governing equations for both the SIR and SIS epidemic models on \emph{networks}. Although SIR and SIS are basic epidemic models, deductions from their exact stochastic equations \textbf{without} making approximations (such as the common mean-field approximation) are scarce. An exact analytic solution of the governing equations is highly unlikely to be found (for any network) due...

Topics: Populations and Evolution, Mathematics, Quantitative Biology, Dynamical Systems

Source: http://arxiv.org/abs/1402.1731

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3.0

Jun 30, 2018
06/18

by
F. A. L. Mauguière; P. Collins; G. S. Ezra; S. C. Farantos; S. Wiggins

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A model Hamiltonian for the reaction CH$_4^+ \rightarrow$ CH$_3^+$ + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom...

Topics: Chemical Physics, Physics, Nonlinear Sciences, Statistical Mechanics, Chaotic Dynamics,...

Source: http://arxiv.org/abs/1402.0012

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2.0

Jun 30, 2018
06/18

by
Thierry Paul; Laurent Stolovitch

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We consider some perturbations of a family of pairwise commuting linear quantum Hamiltonians on the torus with possibly dense pure point spectra. We prove that the Rayleigh-Schr{\"o}dinger perturbation series converge near each unperturbed eigenvalue under the form of a convergent quantum Birkhoff normal form. Moreover the family is jointly diagonalised by a common unitary operator explicitly constructed by a Newton type algorithm. This leads to the fact that the spectra of the family...

Topics: Mathematics, Analysis of PDEs, Mathematical Physics, Dynamical Systems

Source: http://arxiv.org/abs/1402.2957

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2.0

Jun 30, 2018
06/18

by
Artur Avila; Pascal Hubert; Alexandra Skripchenko

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We study chaotic plane sections of some particular family of triply periodic surfaces. The question about possible behavior of such sections was posed by S. P. Novikov. We prove some estimations on the diffusion rate of these sections using the connection between Novikov's problem and systems of isometries - some natural generalization of interval exchange transformations. Using thermodynamical formalism, we construct an invariant measure for systems of isometries of a special class called the...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1412.7913

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2.0

Jun 30, 2018
06/18

by
Fernando Jimenez; Juergen Scheurle

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In this paper we explore the nonholonomic Lagrangian setting of mechanical systems in local coordinates on finite-dimensional configuration manifolds. We prove existence and uniqueness of solutions by reducing the basic equations of motion to a set of ordinary differential equations on the underlying distribution manifold $D$. Moreover, we show that any $D-$preserving discretization may be understood as beeing generated by the exact evolution map of a time-periodic non-autonomous perturbation...

Topics: Mathematics, Numerical Analysis, Mathematical Physics, Dynamical Systems

Source: http://arxiv.org/abs/1407.2116

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2.0

Jun 30, 2018
06/18

by
Georgi S. Medvedev; Xuezhi Tang

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The Kuramoto model (KM) of coupled phase oscillators on complete, Paley, and Erdos-Renyi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER graphs share many structural properties. For instance, they exhibit the same asymptotics of the edge distributions, homomorphism densities, graph spectra, and have constant graph limits. Nonetheless, we show that the asymptotic behavior of solutions in the KM on these graphs can be qualitatively different. Specifically,...

Topics: Nonlinear Sciences, Quantitative Biology, Neurons and Cognition, Mathematics, Pattern Formation and...

Source: http://arxiv.org/abs/1407.3990

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3.0

Jun 30, 2018
06/18

by
Boris Solomyak

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We study the connectedness locus N for the family of iterated function systems of pairs of affine-linear maps in the plane (the non-self-similar case). First results on the set N were obtained in joint work with P. Shmerkin (2006). Here we establish rigorous bounds for the set N based on the study of power series of special form. We also derive some bounds for the region of "*-transversality" which have applications to the computation of Hausdorff measure of the self-affine attractor....

Topics: Mathematics, Classical Analysis and ODEs, Dynamical Systems

Source: http://arxiv.org/abs/1407.2563

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2.0

Jun 30, 2018
06/18

by
Matthieu Arfeux

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We study sequences of analytic conjugacy classes of rational maps which diverge in moduli space. In particular, we are interested in the notion of rescaling limits introduced by Jan Kiwi. In the continuity of [A1] we recall the notion of dynamical covers between trees of spheres for which a periodic sphere corresponds to a rescaling limit. We study necessary conditions for such a dynamical cover to be the limit of dynamically marked rational maps. With these conditions we classify them for the...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1408.2118

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2.0

Jun 30, 2018
06/18

by
Cheng Yang; Xiaoping Yuan

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To study the variation problem related to the incompressible fluid mechanics, Brenier brings the concept of generalized flow and shows that the generalized incompressible flow (GIF) is deeply related to the classical solution of the incompressible Euler equations. In this paper, we will study the ergodic theory of the GIF which may help us understand the dynamic property of the classical solution of the incompressible Euler equations. First, we show that the GIF has the weak recurrent property...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1408.2659

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4.0

Jun 29, 2018
06/18

by
Manon Baudel; Nils Berglund

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We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain, called a random Poincar\'e map, which encodes the metastable behaviour of the system. We show that this process admits exactly $N$ eigenvalues which are exponentially close to $1$, and provide expressions for these eigenvalues and their left and right...

Topics: Probability, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1611.04869

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3.0

Jun 30, 2018
06/18

by
Nicolas Bédaride; Thomas Fernique

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On the one hand, Socolar showed in 1990 that the n-fold planar tilings admit weak local rules when n is not divisible by 4 (the n=10 case corresponds to the Penrose tilings and is known since 1974). On the other hand, Burkov showed in 1988 that the 8-fold tilings do not admit weak local rules, and Le showed the same for the 12-fold tilings (unpublished). We here show that this is actually the case for all the 4p-fold tilings.

Topics: Mathematics, Discrete Mathematics, Computing Research Repository, Mathematical Physics, Dynamical...

Source: http://arxiv.org/abs/1409.0215

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2.0

Jun 30, 2018
06/18

by
Ruta Mehta; Ioannis Panageas; Georgios Piliouras

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In a recent series of papers a surprisingly strong connection was discovered between standard models of evolution in mathematical biology and Multiplicative Weights Updates Algorithm, a ubiquitous model of online learning and optimization. These papers establish that mathematical models of biological evolution are tantamount to applying discrete Multiplicative Weights Updates Algorithm, a close variant of MWUA, on coordination games. This connection allows for introducing insights from the...

Topics: Quantitative Biology, Mathematics, Quantitative Methods, Computing Research Repository,...

Source: http://arxiv.org/abs/1408.6270

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2.0

Jun 30, 2018
06/18

by
Alessandro Fortunati; Stephen Wiggins

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The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly-integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically vanishing. The paper is an extension of an analogous result by the same authors for canonical Hamiltonian systems; the flexibility of the Lie series method developed by A. Giorgilli et al., is profitably used in the present generalisation.

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1409.0430

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2.0

Jun 30, 2018
06/18

by
Getachew K. Befekadu; Panos J. Antsaklis

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In this paper, we consider a diffusion process pertaining to a chain of distributed control systems with small random perturbation. The distributed control system is formed by n subsystems that satisfy an appropriate Hormander condition, i.e., the second subsystem assumes the random perturbation entered into the first subsystem, the third subsystem assumes the random perturbation entered into the first subsystem then was transmitted to the second subsystem and so on, such that the random...

Topics: Mathematics, Probability, Dynamical Systems

Source: http://arxiv.org/abs/1408.6260

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2.0

Jun 30, 2018
06/18

by
Shirali Kadyrov

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It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension of exceptional sets arising from dynamics.

Topics: Mathematics, Number Theory, Dynamical Systems

Source: http://arxiv.org/abs/1409.0946

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Jun 30, 2018
06/18

by
Giulio Tiozzo

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The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends to complex polynomials the entropy theory for real unimodal maps: the real segment is replaced by an invariant tree, known as Hubbard tree, which lives inside the filled Julia set. We prove that the core entropy of quadratic polynomials varies...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1409.3511

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2.0

Jun 30, 2018
06/18

by
Liang Kong; Nar Rawal; Wenxian Shen

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The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a system is first introduced via the natural features of spreading speeds. The existence and lower bounds of spreading speed intervals are then established. When the periodic dependence of the habitat is only on the time variable, the existence of a single...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1410.0317

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Jun 30, 2018
06/18

by
Jason Siefken

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The Kari-Culik tilings are formed from a set of 13 Wang tiles that tile the plane only aperiodically. They are the smallest known set of Wang tiles to do so and are not as well understood as other examples of aperiodic Wang tiles. We show that the $\mathbb{Z}^2$ action by translation on a certain subset of the Kari-Culik tilings, namely those whose rows can be interpreted as Sturmian sequences (rotation sequences), is minimal. We give a characterization of this space as a skew product as well...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1410.1572

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2.0

Jun 30, 2018
06/18

by
Carlo Carminati; Giulio Tiozzo

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We consider for each t the set K(t) of points of the circle whose forward orbit for the doubling map does not intersect (0,t), and look at the dimension function eta(t) := H.dim K(t). We prove that at every bifurcation parameter t, the local Hoelder exponent of the dimension function equals the value of the function eta(t) itself. The same statement holds by replacing the doubling map with the map g(x) := dx mod 1 for d >2.

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1410.5761

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2.0

Jun 30, 2018
06/18

by
Matthieu Astorg; Xavier Buff; Romain Dujardin; Han Peters; Jasmin Raissy

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We show that there exist polynomial endomorphisms of C^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P^2(C). We also find real examples with wandering domains in R^2. The proof is based on parabolic implosion techniques, and is based on an original idea of M. Lyubich.

Topics: Complex Variables, Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1411.1188

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2.0

Jun 30, 2018
06/18

by
Ryokichi Tanaka

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For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times the logarithmic volume growth if and only if the corresponding harmonic measure is comparable with Hausdorfff measure on the boundary. Moreover, we introduce one parameter family of probability measures which interpolates a Patterson-Sullivan measure and the harmonic measure, and establish a formula of Hausdorff...

Topics: Probability, Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1411.2312

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3.0

Jun 30, 2018
06/18

by
Elise Goujard

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We present an explicit formula relating volumes of strata of meromorphicquadratic differentials with at most simple poles on Riemann surfacesand counting functions of the number of flat cylinders filled by closedgeodesics in associated flat metric with singularities. This generalizes the resultof Athreya, Eskin and Zorich in genus 0 to higher genera.

Topics: Dynamical Systems, Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1405.5899

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2.0

Jun 30, 2018
06/18

by
Amichai Eisenmann; Yair Glasner

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Let $E$ be a measure preserving equivalence relation, with countable equivalence classes, on a standard Borel probability space $(X,B,\mu)$. Let $([E],d_{u})$ be the the (Polish) full group endowed with the uniform metric. If $F_r = \langle s_1, \ldots, s_r \rangle$ is a free group on $r$-generators and $\alpha \in \operatorname{Hom}(F_r,[E])$ then the stabilizer of a $\mu$-random point $\alpha(F_r)_x$ is a random subgroup of $F_r$ whose distribution is conjugation invariant. Such an object is...

Topics: Dynamical Systems, Mathematics, Group Theory

Source: http://arxiv.org/abs/1406.1261

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3.0

Jun 30, 2018
06/18

by
Nicola Guglielmi; Linda Laglia; Vladimir Protasov

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We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in relatively high dimensions. The same technique is also extended for stabilizability of positive systems by evaluating a polytope concave Lyapunov function ("antinorm") in the cone. The method is based on a suitable discretization of the underlying continuous...

Topics: Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1406.5927